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Location choice and risk attitude of a decision maker

OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2017年第PartA期66卷 170-181页

作者： Berman, Oded Sanajian, Nima Wang, Jiamin Univ Toronto Joseph L Rotman Sch Management 105 St George St Toronto ON M5S 3E6 Canada Long Isl Univ Coll Management Post Campus720 Northern Blvd Greenvale NY 11548 USA

In this paper we study the effect of a decision maker's risk attitude on the median and center problems, two well-known location problems, with uncertain demand in the mean-variance framework. We provide a mathematical programming formulation for both problems in the form of quadratic programming and develop solution procedures. In particular, we consider the vertex and absolute median problems separately, and identify a dominant set for the center problem. Glover's linearization method is applied to solve the vertex median problem. We also develop a branch and bound algorithm and a heuristic as the linearization technique takes too long for the vertex median problem on large networks. A computational experiment is conducted to compare the performance of the algorithms. We demonstrate the importance of taking into account the volatility and correlation structure when a location decision is made. The closest assignment property is also discussed for these location problems under the mean-variance objective. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Facility location mixed-integer quadratic programming quadratic assignment problem Mean-variance Risk-averse Risk-seeking

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Exact mixed-integer quadratic formulation and solution for large-scale thermal unit commitment

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INTERNATIONAL JOURNAL OF LOW-CARBON TECHNOLOGIES 2024年第19期19卷 1003-1012页

作者： Kang, Chuanxiong Wang, Yongwen Wu, Shaofei Ding, Guili Chen, Chen Nanchang Inst Technol Natl & Prov Joint Engn Lab Hydraul Engn Safety & E 289 Tianxiang Rd Nanchang 330099 Peoples R China Nanchang Inst Technol Jiangxi Engn Res Ctr High Power Elect & Grid Smart 289 Tianxiang Rd Nanchang 330099 Peoples R China China Renewable Energy Engn Inst 57 Andingmenwai St Beijing 100120 Peoples R China

Thermal unit commitment (UC) is a nonlinear combinatorial optimization problem that minimizes total operating costs while considering system load balance, on/off restrictions and other constraints. Successfully solving the thermal UC problem contributes to a more reliable power system and reduces thermal costs. This paper presents an exact mixed-integer quadratic programming (EMIQP) method for large-scale thermal UC problems. EMIQP revolutionizes the landscape by seamlessly translating the intricate nonlinear combinatorial optimization problem of UC into an exact mixed-integer quadratic formulation. This approach also elegantly reimagines on/off constraints as mixed-integer linear equations, employing both the sum and respective approaches. Our case studies unequivocally demonstrate the exceptional prowess of the EMIQP method, consistently securing the global optimum. Moreover, the mathematical-based EMIQP method produces identical results at each run, which is extremely important for UC in the real world.

关键词： thermal unit commitment nonlinear combinatorial optimization mixed-integer quadratic programming exact formulation

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Moving horizon estimation for hybrid systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2002年第10期47卷 1663-1676页

作者： Ferrari-Trecate, G Mignone, D Morari, M Swiss Fed Inst Technol Swiss Fed Inst Technol Inst Automat CH-8092 Zurich Switzerland

We propose a state-smoothing algorithm for hybrid systems based on moving-horizon estimation (MHE) by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems. We provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the MHE scheme. Moreover, we propose two practical algorithms for the computation of penalties that allow to implement MHE by solving a mixed-integer quadratic program.

关键词： hybrid systems mixed-integer quadratic programming observability piecewise affine systems state estimation

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Algorithm for cardinality-constrained quadratic optimization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2009年第1期43卷 1-22页

作者： Bertsimas, Dimitris Shioda, Romy Univ Waterloo Dept Combinator & Optimizat Fac Math Waterloo ON N2L 3G1 Canada MIT Alfred P Sloan Sch Management Cambridge MA 02139 USA MIT Ctr Operat Res Cambridge MA 02139 USA

This paper describes an algorithm for cardinality-constrained quadratic optimization problems, which are convex quadratic programming problems with a limit on the number of non-zeros in the optimal solution. In particular, we consider problems of subset selection in regression and portfolio selection in asset management and propose branch-and-bound based algorithms that take advantage of the special structure of these problems. We compare our tailored methods against CPLEX's quadratic mixed-integer solver and conclude that the proposed algorithms have practical advantages for the special class of problems we consider.

关键词： mixed-integer quadratic programming Branch-and-bound Lemke's method Subset selection Portfolio selection

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Convex Models of Distribution System Reconfiguration

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IEEE TRANSACTIONS ON POWER SYSTEMS 2012年第3期27卷 1407-1413页

作者： Taylor, Joshua A. Hover, Franz S. Univ Calif Berkeley Dept Elect Engn & Comp Sci Berkeley CA 94720 USA MIT Dept Mech Engn Cambridge MA 02139 USA

We derive new mixed-integer quadratic, quadratically constrained, and second-order cone programming models of distribution system reconfiguration, which are to date the first formulations of the ac problem that have convex, continuous relaxations. Each model can be reliably and efficiently solved to optimality using standard commercial software. In the course of deriving each model, we obtain original quadratically constrained and second-order cone approximations to power flow in radial networks.

关键词： Distribution system reconfiguration load balancing mixed-integer quadratic programming second-order cone programming

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IMPROVED ALGORITHM FOR mixed-integer quadratic PROGRAMS AND A COMPUTATIONAL STUDY

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MATHEMATICAL programming 1985年第1期32卷 100-113页

作者： LAZIMY, R 1.The Hebrew University Jerusalem Israel

In a recent paper [6] we suggested an algorithm for solving complicated mixed-integer quadratic programs, based on an equivalent formulation that employs a nonsingular transformation of variables. The objectives of the present paper are two. First, to present an improved version of this algorithm, which reduces substantially its computational requirements; second, to report on the results of a computational study with the revised algorithm.

关键词： mixed-integer quadratic programming quadratic Duality Theory Generalized Benders Decomposition

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Critical node detection problem for complex network in undirected weighted networks

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2020年 538卷 122862-122862页

作者： Chen, Wei Jiang, Manrui Jiang, Cheng Zhang, Jun Capital Univ Econ & Business Sch Management & Engn Beijing Peoples R China

Detection of critical nodes in complex networks has recently received extensive attention. Currently, studies of the critical nodes problem (CNP) mainly focus on two problem types: "critical nodes problem/positive" (CNP-Pos) and "critical nodes problem/negative" (CNP-Neg). However, to the best of our knowledge, few studies have been conducted on CNP-Neg for weighed networks. In this paper, we investigate CNP-Neg in undirected weighted networks. We first propose a novel metric D-FW to evaluate network fragmentation. Then, we formulate a new nonconvex mixed-integer quadratic programming model, named MIQPM, that aims to simultaneously minimize pairwise connectivity and maximize the weights between the nodes. After that, a general greedy algorithm is employed to solve the corresponding optimization problem. Finally, comparison experiments are carried out for several synthetic networks and four real-world networks to demonstrate the effectiveness of the proposed approaches. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Critical nodes problem Weighted network Network fragmentation mixed-integer quadratic programming Greedy algorithm

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Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex quadratic Programs with Applications in Network Infrastructure Planning

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NETWORKS & SPATIAL ECONOMICS 2011年第1期11卷 159-191页

作者： Li, Mian Gabriel, Steven A. Shim, Yohan Azarm, Shapour Univ Maryland Appl Math & Stat & Sci Computat Program College Pk MD 20742 USA Shanghai Jiao Tong Univ Univ Michigan Joint Inst Shanghai 200240 Peoples R China Univ Maryland Dept Civil & Environm Engn College Pk MD 20742 USA Univ Maryland Dept Mech Engn College Pk MD 20742 USA

Planning infrastructure networks such as roads, pipelines, waterways, power lines and telecommunication systems, require estimations on the future demand as well as other uncertain factors such as operating costs, degradation rates, or the like. When trying to construct infrastructure that is either optimal from a social welfare or profit perspective (depending on a public or private sector focus), typically researchers treat the uncertainties in the problem by using robust optimization methods. The goal of robust optimization is to find optimal solutions that are relatively insensitive to uncertain factors. This paper presents an efficient and tractable approach for finding robust optimum solutions to linear and, more importantly, quadratic programming problems with interval uncertainty using a worst case analysis. For linear, mixed-integer linear, and mixed-integer problems with quadratic objective and constraint functions, our robust formulations have the same complexity and tractability as their deterministic counterparts. Numerous examples with differing difficulties and complexities, especially with selected ones on network planning/operations problems, have been tested to demonstrate the viability of the proposed approach. The results show that the computational effort of the proposed approach, in terms of the number of function calls, for the robust problems is comparable to or even better than that of deterministic problems in some cases.

关键词： Robust optimization Interval uncertainty Linear programming quadratic programming mixed-integer linear programming mixed-integer quadratic programming

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Optimization of raw material procurement at pulp or paper mills - the influence of weather-related risks

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2006年第4期37卷 253-269页

作者： Hultqvist, D Olsson, L Mid Sweden Univ Fibre Sci & Commun Ctr SE-85170 Sundsvall Sweden

There are usually many sources for the supply of raw material to a pulp or paper mill in Sweden. Optimization of this supply is therefore a challenging task, and can only be managed properly if all aspects of risk are considered. In our study, these risks are related to when the weather reduces the load-bearing capacity of the ground or the roads. A stochastic and a deterministic model have been formulated, and they have been solved with mixed-integer quadratic programming and tested with data from a Swedish forest company. The results of this study show that the option value is greater than zero and that both the optimal policy and the option value change whenever the storage cost is altered. This shows that the optimal planning policy obtained from the stochastic model differs from the solution of the deterministic model.

关键词： mixed-integer quadratic programming real options forest logistics multi-commodity networks multi-modality

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How to convexify the intersection of a second order cone and a nonconvex quadratic

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MATHEMATICAL programming 2017年第1-2期162卷 393-429页

作者： Burer, Samuel Kilinc-Karzan, Fatma Univ Iowa Dept Management Sci Iowa City IA 52242 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-that the convex hull of the intersection of an ellipsoid, , and a split disjunction, with , equals the intersection of with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form and , where is a SOCr cone, is a nonconvex cone defined by a single homogeneous quadratic, and H is an affine hyperplane. Under several easy-to-verify conditions, we derive simple, computable convex relaxations and , where is a SOCr cone. Under further conditions, we prove that these two sets capture precisely the corresponding conic/convex hulls. Our approach unifies and extends previous results, and we illustrate its applicability and generality with many examples.

关键词： Convex hull Disjunctive programming mixed-integer linear programming mixed-integer nonlinear programming mixed-integer quadratic programming Nonconvex quadratic programming Second-order-cone programming Trust-region subproblem

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